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Axioms 2013, 2(1), 20-43; doi:10.3390/axioms2010020
Article

Some Modular Relations Analogues to the Ramanujan’s Forty Identities with Its Applications to Partitions

*  and
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore 570 006, India
* Author to whom correspondence should be addressed.
Received: 1 November 2012 / Revised: 22 January 2013 / Accepted: 28 January 2013 / Published: 18 February 2013
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Abstract

Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan’s forty identities for Rogers-Ramanujan functions. Furthermore, we give partition theoretic interpretations of some of our modular relations.
Keywords: Rogers-Ramanujan functions; theta functions; partitions; colored partitions; modular relations Rogers-Ramanujan functions; theta functions; partitions; colored partitions; modular relations
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Adiga, C.; Bulkhali, N.A.S. Some Modular Relations Analogues to the Ramanujan’s Forty Identities with Its Applications to Partitions. Axioms 2013, 2, 20-43.

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